Week 6 Assumptions Part III and Multicollinearity

Question 1

Homoskedasticity

Answer 1

An assumption of equal or similar variances in different groups being compared

This is an important assumption of parametric statistical tests because they are sensitive to any dissimilarities. Uneven variances in samples result in biased and skewed test results.

Question 2

Heteroskedasticity

definition and consequence

Answer 2

Happens when the standard deviations of a predicted variable, monitored over different values of an independent variable or as related to prior time periods, are non-constant.

consequence:
- Inefficiency
- SE is wrong (biased), resulting in unreliable confidence intervals and hypotheses tests.

Question 3

Causes of heteroskedasticity

Answer 3

• Necessary but not sufficient conditions
• Measurement improves with independent variables
• Presence of outliers (An outlier is an observation that lies an abnormal distance from other values in a random sample from a population)
• Specification error (especially omission of relevant variable and nonadditivity)

Question 4

Omission

Answer 4

Samples with invalid data are discarded from further analysis

Question 5

Omitted-variable bias (OVB)

Answer 5

Occurs when a statistical model leaves out one or more relevant variables

Question 6

Weighted Least Squares (WLS)

Answer 6

Weighted least squares is a version of least squares where you give importance (or weight) to some data point over others. In WLS, points with higher weights are considered more reliable, so they have more influence on finding the best-fitting line or model.

In presence of heteroskedasticity, WLS is BLUE

Question 7

Autocorrelation

Answer 7

Measures the relationship between a variable’s current value and it’s past values.

An autocorrelation of +1 represents a perfect positive correlation, while an autocorrelation of -1 represents a perfect negative correlation.

Question 8

Cross-sectional

Answer 8

Observations are recorded for different individuals/objects at one time

Question 9

Time series

Answer 9

Observations are recorded for the same individual/object across time

Question 10

Time series, cross sectional (or repeated cross-sections)

Answer 10

Observations are recorded across time but for different individuals each time

Question 11

Panel

Answer 11

Observations are recorded for the same individuals across time

Question 12

Serial autocorrelation

Answer 12

The correlation between neighbouring observations ordered in time

Question 13

Spatial autocorrelation

Answer 13

The correlation between neighbouring observations ordered in space

Example: crime rates in neighboring city wards

Question 14

Multicollinearity

Answer 14

Occurs when two or more predicotr variables in a regression model are highly correlated, making it hard to determine their individual effects on the outcome. This can lead to unstable estimates and reduce the reliability of the model

Question 15

Perfect multicollinearity

Answer 15

When one independent variable is an exact linear combination of one or more other independent variables. This makes it impossible for the model to estimate unique coefficients for those variables, as they provide the same information

• Results in R2of 1, but indeterminate model (cannot be estimated!)
• Does not violate Gauss-Markov, estimates are still BLUE, but variances are high

Question 16

Dummy variable

Answer 16

A dummy variable is a numerical variable used in regression models to represent categorical data. It takes values of 0 or 1 to indicate the absence or presence of a particular category